## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 22, Number 2 (1951), 165-179.

### Consistency and Unbiasedness of Certain Nonparametric Tests

#### Abstract

It is shown that there exist strictly unbiased and consistent tests for the univariate and multivariate two- and $k$-sample problem, for the hypothesis of independence, and for the hypothesis of symmetry with respect to a given point. Certain new tests for the univariate two-sample problem are discussed. The large sample power of these tests and of the Mann-Whitney test are obtained by means of a theorem of Hoeffding. There is a discussion of the problem of tied observations.

#### Article information

**Source**

Ann. Math. Statist., Volume 22, Number 2 (1951), 165-179.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177729639

**Digital Object Identifier**

doi:10.1214/aoms/1177729639

**Mathematical Reviews number (MathSciNet)**

MR40632

**Zentralblatt MATH identifier**

0045.40903

**JSTOR**

links.jstor.org

#### Citation

Lehmann, E. L. Consistency and Unbiasedness of Certain Nonparametric Tests. Ann. Math. Statist. 22 (1951), no. 2, 165--179. doi:10.1214/aoms/1177729639. https://projecteuclid.org/euclid.aoms/1177729639